1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Partial fraction (tricky stuff for LaPlace transforms)

  1. Jul 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Doing some Laplace transform stuffs and I've got [tex]Y(s) = \frac{1}{(s+1)(s^{2}+2s+2)}[/tex]

    Using the normal method

    [tex]1 = A((s+1)^{2}+1) + B(s+1)[/tex]

    I'm not sure this method is valid though as we had a complicated term (s+1)² + 1 after A. I can find A to be 1, but I don't trust my value of B being -1.

    Apparently the answer is [tex]\frac{1}{s+1} - \frac{s+1}{(s+1)^{2}+1}[/tex]

    Not sure how to get there though

  2. jcsd
  3. Jul 28, 2010 #2
    The discrimant of the quadratic trinomial is:

    \Delta = 1^{2} - 1 \cdot 2 = 1 - 2 = -1 < 0

    so it does not have real zeros. That is why the partial fraction expansion is of the form:

    \frac{1}{(s + 1)(s^{2} + 2 s + 2)} = \frac{A}{s + 1} + \frac{B s + C}{s^{2} + 2 s + 2}

    Multiply both sides by [itex](s + 1)(s^{2} + 2 s + 2)[/itex], collect terms with like powers of s on the right hand side and compare the corresponding coefficients so that you will get three equations for the three unknowns A, B and C. Also, complete the square for the trinomial:

    s^{2} + 2 s + 2

    You should get the answer you were looking for.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook